A growth window for the Mn effusion cell temperature (TMn) is demonstrated for epitaxial Mn-doped ZnO (MnZnO) thin films grown on sapphire substrates using molecular-beam epitaxy. Within the growth window, the films are ferromagnetic with the largest saturated magnetization occurring at TMn=700 °C. The Curie temperature of these MnZnO diluted magnetic semiconductor thin films is above room-temperature. The ferromagnetism is weakly anisotropic. Well-resolved near-band-edge photoluminescence emissions dominate the spectra at both low- and room-temperatures. No evident spin polarization on the carriers was detected with the magneto-photoluminescence studies. Magnetoresistance and anomalous Hall effects of the MnZnO thin films were studied. The anomalous Hall coefficient shows a quadratic dependence on the resistivity.